Errand of the heart captured husband (5)
I believe the answer is:
chore
'errand' is the definition.
(I've seen this in another clue)
'heart captured husband' is the wordplay.
'heart' becomes 'core' (synonyms).
'captured' indicates putting letters inside.
'husband' becomes 'h' (abbreviation).
'core' placed around 'h' is 'CHORE'.
'of the' is the link.
(Other definitions for chore that I've seen before include "Household job" , "Drudgery" , "burden" , "Mundane task" , "Manipulate; name" .)